In recent years, decentralized stochastic optimization has become a popular research topic in the signal processing and machine learning communities. With the rapidly increasing number of distributed devices and volume of generated data, traditional signal processing and machine learning approaches, which rely on a central controller to collect the data samples or coordinate the optimization process, suffer from privacy and scalability issues [1]}. In decentralized stochastic optimization, every device (called as agent thereafter) learns its own model using its local data samples, and periodically exchanges its model with neighboring agents so as to achieve consensus. This scheme is favorable in privacy preservation since the data samples are kept local, and does not rely on any central controller that could be a system bottleneck. Existing decentralized stochastic optimization methods include decentralized parallel stochastic gradient descent (DPSGD) [2]}, stochastic subgradient projection [3]}, dual averaging [4]}, mirror descent [5]}, etc. Asynchronous algorithms are developed in [6]}, [7]} to reduce the idle time, and variance reduction techniques are proposed in [8]}, [9]}, [10]}, [11]}, [12]} to improve the convergence rate. Decentralized stochastic optimization methods are shown to be superior to their centralized counterparts on training large-scale neural networks when the communication links are subject to high latency and limited bandwidth [13]}.
